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Updated on: 26 Jul 2014, 15:13

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26 Jul 2014, 10:23

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Here is a Tip on work/rate problems. I would like to introduce Percent approach to solve Work/rate problems.

Let's consider basic example.A can complete a certain task in 10 hours and B can complete the same task 20 hours. We assume that the task is 100% So if A can complete the task in 10 hours, we can say he is taking 10 hours to complete 100% of task. That means in one hour he is finishing \(\frac{100%}{10}\) or 10% task.Similarly B is completing \(\frac{100%}{20}\) or 5% task in one hour.If they start working together(at their respective rates), they would finish (10% + 5%) or 15% task in one hour. So to finish entire task together, it would take them \(\frac{100}{15}\) or \(6\frac{2}{3}\) hours.

Three workers, A, B, and C, can complete a certain task in 10, 5 and x hours respectively. A starts working alone and 2 hours later B joins. After another 2 hours joins C. After that A, B, and C together complete the task in 15 minutes. What is the value of x?

A. 1B. 1.25C. 2D. 2.5E. 4

Three workers, A, B, and C, can complete a certain task in 10, 5 and x hours respectivelySo in one hour A is completing 10% task, B is completing 20% task, and C is completing \((\frac{100}{x})%\) task.

A starts working alone and 2 hours later B joins.Before B joins, A will have worked for 2 hours and have finished 20% task. That means when B joins A, total remaining work will be 80%

After another 2 hours joins C.Using Similar logic, At the time of C's joining, A & B will have finished 60% task. Remaining work will be 20%

After that A, B, and C together complete the task in 15 minutes.So A, B, C together complete remaining 20% task in 15 mins or in \(\frac{15}{60} hours\)